1. Field of the Invention
The present invention relates to a method and apparatus for modeling molecules. In another aspect, the present invention relates to a method and apparatus for modeling molecules undergoing change between conformational states. In even another aspect, the present invention relates to a method and apparatus for modeling the 2D-NOESY spectra of interacting systems undergoing multistate conformational exchange.
2. Description of the Related Art
The analysis of nuclear Overhauser effects ("NOE") in multispin systems by the use of isolated spin pair approximation ("ISPA") is often inadequate since it neglects multispin effects, i.e., three spin effects for small molecules with short correlation times, and spin diffusion effects for large molecules with longer rotaional correlation times. See, Krishna et al., Biophys. J., 24:791 (1978). To get meaningful structural information on macromolecules, it is necessary to take these effects into account properly through a total relaxation matrix analysis of experimental NOE intensities. See, Krishna et al., supra.; Keeper et al., J. Magn. Reson.; 57:404 (1984), Borgias et al., J. Magn. Resort., 79:493 (1988); and see, Borgias et al., Methods in Enzymology, 176:169 (1989). In order to systematically account for these effects in the analysis of 2D-NOESY spectra, and to gain precise structural information of nucleic acids and proteins, algorithms based on complete relaxation matrix analyses ("CORMA") have been developed. In one such algorithm a total relaxation matrix methodology is utilized where experimental NOEs can be compared with those predicted for different models using NOE R-factors. See, Krishna et al., supra. Many other variations of complete relaxation matrix analyses of NOESY intensities have been proposed. See, Boelens et al., J. Mol. Struct., 173:299 (1988); Post et al., J. Amer. Chem. Soc., 112:6796 (1990); Mertz et al., J. Biomol. NMR, 1:257(1991); and Sugar et al., Prog. Biophys. Molec. Biol., 58:61 (1992). In all these treatments, there is usually the assumption of a single conformation for the macromolecule under consideration.
When the macromolecular system exhibits a conformational exchange as well, as in the case of a ligand exchanging between free and enzyme-bound forms, a protein interacting with DNA, or a protein existing in equilibrium between distinct conformations, it is necessary to incorporate properly such exchange effects in a complete relaxation matrix analysis. See, Choe et al., J. Magn. Reson. 94:387. A preliminary account of a formalism for complete relaxation and conformational exchange matrix ("CORCEMA") has been suggested. See, Lee et al., J. Magn. Reson. 98:36 (1992), and see, Krishna et al., Biophys. J. 61:A33 (1992). This work presented the general theory for a multispin system exchanging between two states, and illustrated its application with simulated examples of a DNA fragment exchanging between right and left handed forms, and a transferred NOESY analysis of a pair of ligand protons exchanging between free and enzyme-bound forms.
In literature so far, the primary focus of transferred NOESY analysis has been to deduce the conformation of a small ligand (e.g., an inhibitor) when it is bound to a much larger protein (such as an enzyme). Several examples along with the current status of this method have been reviewed recently. See, F. Ni, Prog. NMR Spectroscopy, 26:517 (1994). When the binding between the ligand and the protein is tight (with K.sub.d.sup..about. 10.sup.-9 M), direct study of the ligand in its complexed form is utilized. However, when the binding constant is somewhat weaker, it is possible to deduce the bound conformation from a study of the free ligand resonances since the cross relaxation information in the bound state is transferred to the free state when the enzyme off-rates are comparable to or faster than the relaxation rates in the bound form. The theory for steady state 1D-transferred NOEs is known, see, Clore et al., J. Magn. Reson. 48:402(1982), and it has been extended to selective saturation-based time dependent transferred NOEs with an emphasis on an analysis of initial slopes, see, Clore et al., J. Magn. Reson. 53:423(1983). Under these conditions, useful structural information in the bound state is obtained if the conformational exchange is fast on the relaxation rate scale.
Four major factors that need to be considered in a relaxation matrix analysis of tr-NOESY are: (i) the possibility of extracting meaningful structural information from a time-course analysis (rather than depending only on initial slopes) of the NOESY spectra even when the off- and on-rates are not fast on the relaxation rate scale, thus significantly extending the range of utility of the tr-NOESY technique; (ii) the ability to quantitatively account for intermolecular ligand-protein cross relaxation in the bound state; (iii) the possibility that the large protein or enzyme may exhibit a binding mode different from the traditional rigid lock-and-key type of fit for the ligand; and (iv) multiple conformations of the bound ligand. Additional minor factors include multiple binding sites on the enzyme as well as nonspecific binding.
The issue in the first factor, analysis of tr-NOESY when the off-rates are comparable to relaxation rates, is recognized in the art, with general theoretical frame works disclosed. See, Lee et al., J. Magn. Reson. 98:36 (1992); Krishna et al., Biophys. J. 61:A33(1992); Ni, J. Magn. Reson. 96:651(1992); London et al., J. Magn. Reson. 97:79(1992); and Lippens et al., J. Magn. Reson. 99:268(1992). The main advantage of these formulations is that the utility of the tr-NOESY technique is now extended to a much wider range of off- and on-rates, rather than restrictive regime of exchange rates faster than the relaxation rates. This is significant because large molecular weight enzyme complexes are characterized by larger cross-relaxation rates which may become comparable to enzyme off-rates. All these theoretical formulations have been cast for treating multispin systems.
Many traditional analyses of tr-NOE experiments have routinely neglected ligand-protein intermolecular cross relaxation, partly because: (a) there was no adequate theoretical frame work available to account for them, (b) it simplified the analyses considerably, and (c) in some instances the structure of the enzyme was presumably unknown and hence it was difficult to take this cross relaxation into account. In some cases, it may be possible to selectively saturate the protein resonances to minimize protein-mediated spin diffusion effects. See, Clore et al., J. Magn. Reson. 53:423(1983).
Of course, any serious effort on a structure-based design of a protein-binding ligand will substantially benefit from the ability to explicitly incorporate the intermolecular contacts with the protein, rather than suppressing them or ignoring them. This is because the conformation of the active site it self can change substantially depending upon the different chemical modifications on the ligand. Such a situation has been recently observed during the design of a series of purine nucleotide phosohorylase inhibitors. See, Ealick et al., Proc. Nat'l. Acad. Sci. USA, 88:11540(1991). In those instances where one is constrained to work with very dilute concentrations (i.e., undetectable) of an enzyme, a common situation in traditional tr-NOE applications, a good starting point for these kind of calculations is provided by the crystallographic data on some known homologus enzymes and enzyme-ligand complexes. Alternatively, if the enzyme is amenable to over expression and isotope labelling by recombinant methods, it may be desirable to work with lower ligand/enzyme ratios to be able to observe the ligand or enzyme resonances by isotope filtered/directed NMR methods. Neglect of ligand-protein interactions can lead to misleading conclusions about the bound conformation of the ligand.
An implicit assumption usually made is that the bound conformation deduced by the tr-NOESY technique corresponds directly to that of the ligand bound in the active site. Indeed, such an assumption is not unreasonable either (i) if the active site with and without the ligand remains essentially identical (e.g., neuraminidase, see Janakiraman et al)., Biochemistry, 33:8172(1994)) as in the rigid lock-and-key model, or (ii) when the process of ligand binding to and release from the active site (into the solvent) is instantaneous.
Complications do arise, however, when the ligand binding process does not follow the rigid lock-and-key model, and the active site on the enzyme exhibits distinct conformational movements following the initial binding of a ligand. These motions can be fast (motion of sidechains) or slow (domain motions). Indeed, enzymes such as thermolysin and related neutral proteases exhibit hinge-bending motion upon binding to inhibitor. See, Holland et al., Biochemistry 31:11310(1992). Similar hinge-bending motions were observed in a class of periplasmic proteins. See, Quiocho, Current Opinion in Structural Biology 1:922(1991). Other known examples are as follows. The maltodextrin binding protein (MBP), a "Venus flytrap" type of rigid-body hinge-bending motion of two globular domains through an angle of 35.degree. has been described upon ligand binding. An examination of the crystal structure of yeast hexokinase-glucose complex shows clearly that the substrate in the active site is essentially shielded from the solvent. In order for it to be released, the cleft formed by the two domains of the enzyme need to open up first--a process that clearly takes finite time. Adenylate kinase provides a very dramatic example since the binding of AMP and ATP (at two separate sites) involves separate domain motions over 39.degree. and 92.degree.. The driving force for such conformational changes presumably is provided by the exclusion of water molecules from the active site by the bound ligand. A hinged "lid" formed by seven residues in triosephosphate isomerase (TIM) moves over 7 .ANG. to close in the substrate in the active site. A somewhat smaller scale movement, the "swinging gate" motion, has been observed in the binding of inhibitors to the human purine-nucleoside phosphorylase. This gate is formed by a 20-residue segment in the enzyme which undergoes a short helical transformation on inhibitor binding. This type of binding belongs to the so called "induced fit" binding, where the active site exhibits considerable fluidity and undergoes conformational changes to accommodate different types of ligands. Another well known example involves carboxypeptidase A, a proteolytic enzyme that hydrolyzes the C-terminal peptide bond in polypeptides. The binding of glycyltyrosine to carboxypeptidase A is accompanied by a structural rearrangement of the enzyme consisting of a nearly 12 .ANG. movement of the phenolic group of Y-248 and smaller movements of 2 .ANG. by R-145 guanidinium and E-270 carboxylate groups. In the case of lysozyme (adsorbed on mica), atomic force microscopy measurements have detected conformational changes of the order of 5 .ANG. lasting for .about.50 ms in the presence of a substrate. All these motions involve a movement of protein domains or a short segment of residues or the sidechains of some residues, to facilitate the ligand in reaching its "final" active site. It is easily appreciated that motions of this type have the potential to modulate the intermolecular ligand-protein NOESY contacts, as well as the intramolecular contacts due to the accompanying conformational changes. Hence there is a clear need to develop a general theory of tr-NOESY that can incorporate such large or small scale protein motions.
Finally, the ligand it self may exhibit conformational transitions while bound to the protein. Hence any attempt to determine the so called bound conformation of a ligand must properly address this conformational malleability of the ligand as well.
The above techniques are not sufficient to model interacting macromolecular systems that are conformationally dynamic.
Additionally, the above techniques are also not sufficient to handle the general n-state conformational exchange case for interacting multispin systems such as a ligand and an enzyme.
Thus, there is a need in the art for improved modeling methods.
There is another need in the art for improved techniques for modeling interacting macromolecular systems that are conformationally dynamic.
There is even another need in the art for improved techniques for modeling the general n-state conformational exchange case for interacting multispin systems such as a ligand and an enzyme.
These and other needs in the art will become apparent to those of skill in the art upon review of this specification, including its claims and drawings.